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Study finds universality in moving cells—a discovery that could impact health and robotics

A study focusing on analyzing cell models found universality in their movement—an important discovery that could impact both health and robotics.
The study "Evidence of universal conformal invariance in living biological matter," with the participation of Nuno Araújo from the Department of Âé¶¹ÒùÔºics at the Faculty of Sciences of the University of Lisbon, has been in Nature Âé¶¹ÒùÔºics.
The starting point for the research was the question: How do individual cells interact with one another without being aware that they are part of a larger whole? The study focused on biological matter and cellular behavior—bringing together two major disciplines: Âé¶¹ÒùÔºics and Biology.
"While in physics we systematically find the same patterns in different systems, in biology, there is always a tendency to think that each system is unique," explains Nuno Araújo, professor and researcher at the Department of Âé¶¹ÒùÔºics at the Faculty of Sciences of the University of Lisbon and one of the study's authors.
Specifically, the research demonstrates that "the collective movement of cells—from systems as diverse as dog kidney cells, human breast cancer cells, or two different types of pathogenic bacteria—exhibits a robust invariance."
The concept may seem complex, but Nuno Araújo uses the visual example of broccoli to simplify the discovery: "A broccoli has the shape of a tree, but if we cut off each branch, it also looks like a tree. If I showed you a picture of each piece and asked which one was the largest, you wouldn't be able to tell. That is scale invariance, and that's what we discovered here. All these systems share the same scale invariance."
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a, Perimeter of contours as a function of their radius of gyration for two prokaryotic and two eukaryotic genotypes, including WT P. aeruginosa bacteria (yellow circles) and a hyperpilated ΔpilH P. aeruginosa mutant (blue squares) that individually move faster, and MDCK cells (red diamonds) and MCF-7 human breast cancer cells (purple stars). b, Variance in the distribution of the winding angle, plotted here as a function of distance along the curve for the four experimental systems and numerical model, all of which exhibit the same logarithmic scaling with a slope of 6/7 (dashed line). Credit: Benjamin H. Andersen, Francisco M. R. Safara, Valeriia Grudtsyna, Oliver J. Meacock, Simon G. Andersen, William M. Durham, Nuno A. M. Araujo & Amin Doostmohammadi -
a, Left-passage probability is defined as the probability that a point in space is on the right side of the contour for a given polar angle. b, Time dependence of the variance of the driving function obtained from a unique conformal slit map. Credit: Benjamin H. Andersen, Francisco M. R. Safara, Valeriia Grudtsyna, Oliver J. Meacock, Simon G. Andersen, William M. Durham, Nuno A. M. Araujo & Amin Doostmohammadi
The researchers focused on four types of cells: two prokaryotic and two eukaryotic. Despite being structurally different, they were found to behave similarly in groups. This opens doors to a greater and deeper understanding of the fundamental matter that constitutes life, leading to numerous potential applications.
The findings could help improve our understanding of oncological diseases and their progression (including metastasis), but also be valuable for tissue engineering, aiding in the development of artificial organs. Additionally, the study provides insights into how bacterial infections spread—potentially leading to better hospital environment management.
These are just a few examples of its impact: in fact, the discovery could also have applications in other systems, such as robotics. As Nuno Araújo explains, it could help improve robot navigation or even influence the development of video games and artificial intelligence systems.
What does this mean? That a form of universality has been identified—something not typically expected in biology. "This opens doors for us to use physics techniques to study biological systems, but also for biological systems to be used to study physical phenomena," says Nuno Araújo.
The study involved the Department of Âé¶¹ÒùÔºics and the Center for Theoretical and Computational Âé¶¹ÒùÔºics at the Faculty of Sciences of the University of Lisbon, as well as several academics from universities in Denmark, Switzerland, and the United Kingdom.
More information: Benjamin H. Andersen et al, Evidence of universal conformal invariance in living biological matter, Nature Âé¶¹ÒùÔºics (2025).
Journal information: Nature Âé¶¹ÒùÔºics
Provided by University of Lisbon